Question

The average unit weight of the uppermost part of the crust is 25000 N/m³. The vertical stress at a depth of 1 km would be MPa. (In integer)

Answer 1

Correct Answer: 25

The vertical stress at a certain depth in the Earth's crust can be calculated using the formula for lithostatic pressure: σ = ρgh, where σ is the vertical stress, ρ is the density or unit weight of the crust, g is the acceleration due to gravity, and h is the depth.

Given:

• Unit weight ρ = 25000 N/m³
• Depth h = 1 km = 1000 m

Acceleration due to gravity, g, is approximately 9.81 m/s². However, since the unit weight ρ already includes gravity, it is not needed explicitly in our calculation for this particular scenario.

We directly use the unit weight (which is force per unit volume) at the given depth:

σ = ρ × h = 25000 N/m³ × 1000 m

σ = 25000000 N/m²

Now, convert the stress from N/m² to MPa (since 1 MPa = 1,000,000 N/m²):

σ = 25000000 N/m² ÷ 1,000,000 = 25 MPa

The vertical stress at a depth of 1 km in the Earth's crust is 25 MPa